She needs a VISA. And given the current geopolitical situation it´s not gonna be easy to get. Even if you land an appointment at the Consulate, you will have to pay the VISA fee and there is no guarantee she´ll get it. Given all the costs involved and the paperwork she will need, maybe the flights that don´t go through the US are not that expensive, from that perspective.

Your girlfriend will 100% need some sort of via if she wants to transit the USA. A more expensive direct flight, or one via Europe or Canada, she probably won't (I assume Canada has a visa free transit system?). If you find a cheap(ish) flight on BA via London, she will need some sort of transit visa, as the LED flight goes into LHR, and the CUN flight leaves from LGW.

If she is going to be visiting you a lot in the US, it might be worth the hassle of getting a US visa.

Quoting Cush (Reply 10):Does anyone have experience with the Mexican "E-Visa" for her and how it works?

It's all done online for Russian, Turkish, and Ukrainian nationals. Fill out an online form not more than 30 days prior to departure (only has a 30-day validity). If granted, you get a sheet to printout and that serves as your visa authorization for the immigration officer.